Permutation & Combination Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Permutations & Combination PRACTICE TEST [1 - EXERCISES]

Permutation & Combination Model Questions Set 1

Question : 16

There are 100 students in a college class of which 36 are boys studying statistics and 13 girls not studying statistics. If there are 55 girls in all, then the probability that a boy picked up at random is not studying statistics, is

a) 1/5

b) 2/5

c) 4/5

d) 3/5

e) None of these

Answer: (a)

There are 55 girls and 45 boys in the college.

Out of 45 boys, 36 are studying Statistics and 9 are not studying statistics.

∴ The probability that a boy picked up at random is not

studying Statistics = $9/{45}$ = $1/5$

Question : 17

In how many ways can six different rings be worn on four fingers of one hand ?

a) 15

b) 12

c) 16

d) 10

e) None of these

Answer: (a)

Required number of ways

= ways of selecting 4 objects out of 6 given objects

= $^6C_4$ = ${6 × 5}/2$ = 15

Question : 18

From amongst 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done ?

a) 1240

b) 1250

c) 1800

d) 1260

e) None of these

Answer: (d)

Principal can be appointed in 36 ways.

Vice principal can be appointed in the remaining 35 ways.

Total number of ways = 36 × 35 = 1260

Question : 19

The committee should consist of 2 Professors, 2 Teachers and 1 Reader?

a) 55

b) 225

c) 90

d) 450

e) None of these

Answer: (d)

Total number of ways to form committee

= $^5C_2 × ^6C_2 × ^3C_1$ = ${5 × 4}/{1 × 2}$ × ${6 × 5}/{1 × 2}$ × $3/1$= 10 × 15 × 3 = 450

Question : 20

In how many different ways can the letters of the word 'OFFICES' be arranged?

a) 1850

b) 5040

c) 1680

d) 2520

e) None of these

Answer: (d)

In word 'offices', there are 7 letters and F comes two times.

Required number of ways = ${7!}/{2!}$ = ${7 × 6 × 5 × 4 × 3 × 2!}/{2!}$ = 2520

IMPORTANT quantitative aptitude EXERCISES

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